930
Research Paper
Interphase chromosomes undergo constrained diffusional
motion in living cells
W.F. Marshall*, A. Straight†, J.F. Marko‡, J. Swedlow§, A. Dernburg*°,
A. Belmont¶, A.W. Murray†, D.A. Agard¥* and J.W. Sedat*
Background: Structural studies of fixed cells have revealed that interphase
chromosomes are highly organized into specific arrangements in the nucleus,
and have led to a picture of the nucleus as a static structure with immobile
chromosomes held in fixed positions, an impression apparently confirmed by
recent photobleaching studies. Functional studies of chromosome behavior,
however, suggest that many essential processes, such as recombination,
require interphase chromosomes to move around within the nucleus.
Results: To reconcile these contradictory views, we exploited methods for
tagging specific chromosome sites in living cells of Saccharomyces cerevisiae
with green fluorescent protein and in Drosophila melanogaster with
fluorescently labeled topoisomerase II. Combining these techniques with
submicrometer single-particle tracking, we directly measured the motion of
interphase chromatin, at high resolution and in three dimensions. We found that
chromatin does indeed undergo significant diffusive motion within the nucleus,
but this motion is constrained such that a given chromatin segment is free to
move within only a limited subregion of the nucleus. Chromatin diffusion was
found to be insensitive to metabolic inhibitors, suggesting that it results from
classical Brownian motion rather than from active motility. Nocodazole greatly
reduced chromatin confinement, suggesting a role for the cytoskeleton in the
maintenance of nuclear architecture.
Conclusions: We conclude that chromatin is free to undergo substantial
Brownian motion, but that a given chromatin segment is confined to a subregion of the nucleus. This constrained diffusion is consistent with a highly
defined nuclear architecture, but also allows enough motion for processes
requiring chromosome motility to take place. These results lead to a model for
the regulation of chromosome interactions by nuclear architecture.
Background
Structural studies of the nucleus demonstrate conclusively
that chromosomes are not scattered randomly in the
nucleus but are, in fact, arranged in a highly defined
nuclear architecture. Particular loci are found reproducibly
at specific nuclear locations [1], suggesting that the nucleus
is a static structure, with chromosomes held rigidly in place
by some sort of nuclear skeleton or matrix. Consistent with
this view, a recent study using fluorescence recovery after
photobleaching (FRAP) indicated that interphase chromatin appears to be essentially immobile at spatial scales
greater than 0.4µm [2]. Experiments in which nuclei were
irradiated with an ultraviolet microbeam and the subsequent position of the damaged DNA was imaged after
various time intervals [3], also indicated that chromatin did
not drift extensively. Furthermore, visualization of chromatin in living cells by time-lapse microscopy does not, in
general, reveal any large, visually obvious, chromatin displacements [4–6]. Thus, both FRAP analysis and direct
Addresses: Departments of *Biochemistry and
Biophysics, †Physiology, §Cellular and Molecular
Pharmacology, University of California at San
Francisco, San Francisco, California 94143, USA.
‡Department of Physics MC273, University of Illinois
at Chicago, Chicago, Illinois 60607-7059, USA.
¶Department of Cell and Structural Biology,
University of Illinois, Urbana-Champaign, Urbana,
Illinois 61801, USA. ¥Howard Hughes Medical
Institute, University of California at San Francisco,
San Francisco, California 94143, USA.
Present addresses: Department of Biology, Yale
University, New Haven, Connecticut 06520, USA.
°Department of Developmental Biology, Stanford
University, Palo Alto, California 94305, USA.
Correspondence: J.W. Sedat
E-mail: [email protected]
Received: 1 September 1997
Revised: 16 October 1997
Accepted: 16 October 1997
Published: 5 November 1997
Current Biology 1997, 7:930–939
http://biomednet.com/elecref/0960982200700930
© Current Biology Ltd ISSN 0960-9822
visualization appear to confirm the suspicion that chromatin may be effectively immobile inside the nucleus.
The picture of the nucleus as a static structure, containing
immobile chromatin held in precise positions, contrasts
strongly with the more dynamic view of chromatin suggested from its behavior. Indeed, movement of chromatin
underlies many essential biological processes including
meiotic homolog pairing, recombination, enhancer looping
and chromosome condensation. We are thus faced with an
apparent contradiction — chromatin is organized into fixed
positions within the nucleus, but it can also move around
inside the nucleus to interact with other regions of chromatin. This raises the possibility that chromatin may actually be mobile, but that the displacements are too small for
FRAP analysis or direct microscopic visualization to detect.
In this report we attempt to resolve this issue by direct
and quantitative tracking of the movement of specific
Research Paper Dynamics of nuclear architecture in vivo Marshall et al.
chromosome regions in real time in living cells of Saccharomyces cerevisiae and Drosophila melanogaster. Our method
involves labeling yeast chromosomes with green fluorescent protein [7,8] or Drosophila chromosomes with microinjected fluorescent topoisomerase II [9], along with threedimensional submicrometer single-particle tracking to
analyze the motion [10,11]. We demonstrate that chromatin
does indeed undergo diffusive random walk motion within
the nucleus, with a diffusion constant large enough to
account for the kinetics of motion-requiring nuclear processes. This diffusive motion is, however, constrained such
that although chromatin can diffuse freely over sufficiently
small spatial scales, a given chromosome region is confined
to a small subregion of the nucleus. This constrained diffusional motion thus reconciles the dynamic behavior of chromatin inferred from functional studies with the high degree
of positional specificity indicated by structural studies.
We consider next the physical basis for the observed
motion. This is especially important when attempting to
understand the mechanism and kinetics of processes, such
as recombination, which require chromatin motion. Is the
passive diffusion of chromatin by Brownian motion sufficiently fast to account for these processes, or is active motility required to move chromatin from one place to another?
The importance of motor-protein-driven motility in
movements of mitotic chromosomes and of cytoplasmic
components, such as vesicles and mitochondria, is well
established. The use of active motility to circumvent the
slow diffusion of large cellular structures is also likely to be
widespread. This issue was first raised for nonmitotic chromosomes by McClintock [12] who pointed out that the
chromosome rearrangements seen during the pairing of
meiotic homologs might require special motile machinery
to pull the chromosomes together, but could potentially
also take place by random diffusion. The large size of the
chromatin polymer, and the density with which it is packed
into the nucleus, suggest that chromatin would diffuse
extremely slowly by Brownian motion [13], leading to the
proposal of more active mechanisms for chromosome movements during homolog pairing [14]. Similarly, for any process that requires movement of chromatin over significant
distances in the nucleus, we must ask whether it could
occur by diffusion alone. In this report, we demonstrate that
chromatin motion continues in the absence of active metabolism, which implies that the motion is due to Brownian
motion and not to active motility. Finally, we demonstrate
that chromatin confinement is microtubule-dependent, a
surprising result that suggests a possible role for the
cytoskeleton in the maintenance of nuclear architecture.
Results
Measuring diffusional motion of chromatin by
sub-micrometer single-particle tracking
To track chromatin in the yeast S. cerevisiae, we visualized
arrays of lac operator sites inserted in the yeast genome, by
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expressing a construct encoding the Lac repressor protein
fused to green fluorescent protein (GFP) [7,8]. Diploid
yeast cells homozygous for an insertion of the lac operator
array into the LEU2 locus near the centromere of chromosome III were imaged in three dimensions as shown in
Figure 1. Only unbudded (G1 phase of the cell cycle) cells
were examined. Cells survived imaging as judged by their
ability to subsequently undergo successful mitotic nuclear
division. Once the position of the lac operator array has
been imaged over time, its diffusion constant can be computed. Determination of a diffusion constant from timelapse images of an object is a well established technique
known as submicrometer single-particle tracking [10,11],
Figure 1
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Visualizing interphase chromatin motion in living yeast cells in three
dimensions. Stereo pairs show successive time-lapse threedimensional images of a diploid yeast cell homozygous for an insertion
of a lac operator array at the LEU2 locus and expressing a GFP–Lac
repressor fusion protein [7]. Relative motion of the two homologous
loci in vivo is clearly evident. Yeast cells imaged under these
conditions remain viable as judged by their ability to bud and undergo
mitotic divisions successfully. Note that the large round object seen
dimly in the background is the whole cell, not the nucleus, and the
background staining represents GFP–LacI molecules in the cytoplasm.
Elapsed time since the beginning of the experiment is given in seconds
to the left of each image. Scale bar = 1 µm.
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and relies on the fact that, by locating the center of mass
of the object in an image, submicrometer displacements
much smaller than the resolution limit of the microscope
[10] can be measured with a precision limited only by the
signal-to-noise ratio of the image.
At each time point, the three-dimensional distance, d(t),
between the two GFP spots was measured. We measured
distance between two spots, rather than the position of a
single spot, in order to compensate for possible drift or
rotation of the nucleus [4,5] which might otherwise lead to
apparent motion. A plot of d(t) for one nucleus is given in
Figure 2a. As the two sites diffuse towards and away from
each other, the distance between them will increase and
decrease at random. Over very short time intervals, the
change in distance will generally be small, whereas over
longer time intervals each site will have diffused more and,
hence, the magnitude of the change will be greater on
average. The average change in distance will thus increase
with increase in time interval [11]. From the relationship
d(t) (µm)
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between the average change in distance and the length of
the time interval, we computed the diffusion constant.
Denoting a time interval by ∆t and the change in distance
d during this interval by ∆d, we computed the mean
squared change in d(t) as 〈∆d2〉 = 〈[d(t) – d(t + ∆t)]2〉. For
two particles undergoing three-dimensional random walks
with diffusion constant D, it can be shown that a plot of
〈∆d2〉 against ∆t should increase linearly [15] with a slope of
4D. A total of 110 data records, each from a different cell,
were averaged and plotted in Figure 2b. Over short time
intervals, we observed a monotonic increase of 〈∆d2〉 with
increasing ∆t, suggesting diffusive motion [11]. Directional
linear motion, such as that produced by motor proteins
translocating on microtubules, would lead to an upwardly
curving parabolic curve for Figure 2b [11], but this was not
evident in our data. Hence we conclude that the chromatin
motion seen is a random walk diffusive motion rather than
a type of directed motility.
For long time intervals, in contrast, the plot in Figure 2b is
horizontal, implying that the average displacement is independent of the time interval. This long-time-scale behavior implies that the diffusion of the two particles is
constrained [11]: each particle is confined to diffuse within
a limited region from which it cannot escape. Such confinement could occur if the chromatin was tethered to the
nuclear envelope or some internal nuclear skeleton. The
plateau height reflects the size of the confinement region,
t (sec)
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Constrained diffusion of chromatin in living yeast cells. (a) Typical data
record obtained by submicrometer single-particle tracking, showing a
plot of the distance between GFP spots d(t) against time t. In such
traces, the distance between spots decreases and increases at
random as the two spots diffuse toward and away from each other. (b)
Overall mean-squared change in distance between GFP spots 〈∆d2〉
plotted against elapsed time interval ∆t between distance
measurements. Solid circles represent living yeast cells; a total of 110
data records, each containing an average of 13 time points, were
combined in this plot. Note that although (a) demonstrates that the
distance between spots both increases and decreases randomly, the
mean-squared change in distance always increases with increasing
time interval [11] — the longer the time interval between measurements,
the more the distance between two diffusing points is expected to
change. For long time intervals, 〈∆d2〉 becomes independent of ∆t and
the plot reaches a plateau, indicating a constraint on diffusion. The
solid line is the best-fit curve derived by computer simulation using
parameters D = 5 × 10–12 cm2/sec and confinement radius R = 0.3 µm
for data from live yeast cells. Solid diamonds, yeast cells fixed in 3.7%
formaldehyde imaged under identical conditions. Motion in living cells
is much greater than in fixed cells, and is thus not due merely to
measurement error. Open circles, chromatin motion in azide-treated
yeast cells showing only slightly reduced motion relative to living cells.
The broken line is the best-fit curve derived using D = 3 × 10–12
cm2/sec and R = 0.25 µm for data from azide-treated cells. (c)
Chromosome diffusion is independent of size: diffusion of a small CEN
plasmid compared to that of a chromosome. Solid circles, motion of
the centromere of chromosome III (reproduced from panel (b) for
comparison). Open circles, motion of CEN plasmid. The broken line is
the best-fit curve derived by computer simulation using
D = 3 × 10–12 cm2/sec, R = 0.25 µm.
Research Paper Dynamics of nuclear architecture in vivo Marshall et al.
while the steepness of the plot at shorter time scales
depends on the diffusion constant [11]. Computer simulations of constrained diffusion were used quantitatively to
relate the slope and plateau height observed in Figure 2b
with the diffusion constant (D) and confinement radius (R)
of the constrained diffusion model. On the basis of such
simulations, we find the data are best described by a particle with D = 5 × 10–12 cm2/sec confined to a region of radius
R = 0.3 µm (root mean square fitting error in 〈∆d2〉 is 4 ×
10–3 µm2). This radius is significantly smaller than the
radius of the diploid nucleus (about 1.5µm), and thus
reflects confinement of the chromatin to a small nuclear
subregion, about one percent of the volume of the nucleus.
Experimental resolution and precision are sufficient for
reliable measurement of chromatin motion
The optical resolution and measurement precision of our
experiments were found to be sufficient to measure chromatin motion reliably. Precision is of particular concern
because random error in the position measurements —
due, for example, to noise in the image or mechanical
jitter in the microscope — would generate data resembling a constrained random walk. To rule out this possibility, we measured the apparent motion in formaldehyde-fixed cells under identical conditions. Intensities,
and hence the signal-to-noise ratios, were the same as for
live cells, leading to equivalent measurement precision.
Any motion seen in fixed cells is due, at least in part, to
limited measurement precision. Motion in fixed cells thus
provides an upper limit on the apparent motion attributable to measurement error. If the apparent motion was
due only to errors in position measurement, then the data
from fixed cells should closely resemble the data from
live cells. As plotted in Figure 2b, motion in living cells
was in fact much greater than in fixed cells, and thus
cannot be due simply to limited measurement precision.
Using data from fixed cells, position measurement error
was estimated to be less than 0.04 µm (see Materials and
methods), which is small relative to the displacements
recorded in living cells. We conclude that measurement
errors are insignificant compared to the actual displacements of the chromatin.
Evaluating alternative models for observed displacements
We have so far presumed that the changes in distance
between labeled sites result from chromatin diffusion.
Several alternative explanations exist, however, and so
must be ruled out. The most obvious possibility is nuclear
rotation [4,5]. If a single focal plane through a cell is
observed, the apparent distance between two spots can
appear to change due to rotation or rocking of the nucleus,
without any actual change in distance between the spots.
This is because a two-dimensional distance measurement
only measures distance in projection, and depends on the
angle of the projection. To avoid this possibility, all
measurements were carried out in three dimensions using
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optical sectioning microscopy. The three-dimensional
distance measurement is unaffected by rotation of the
nucleus and thus provides a more reliable indication of
distance. We can thus immediately rule out nuclear rotation as a cause of the apparent diffusive motion.
Another possible cause of displacement could be forces
exerted on the sample by pressure from the microscope
objective lens. This is of particular concern in threedimensional microscopy because the stage is rapidly
moving up and down. To rule out this possibility, identical
measurements were made in two dimensions by acquiring
a series of images at a fixed focal plane in living cells
without moving the objective or sample; forces exerted on
the sample by the objective lens can thus be eliminated.
The magnitude of the displacements observed in these
two-dimensional experiments is comparable to that seen
in the three-dimensional measurements (data not shown),
and is similarly eliminated when the cells are fixed. We
conclude that the displacements we observe are not
simply a consequence of pressure from the objective lens
on the coverslip.
The constrained motion observed here could, in principle,
be explained if the chromatin was fixed within a nucleus
that was itself undergoing elastic deformations. These
deformations would cause proportional displacements
between any pair of points embedded in the nucleus, and
would give rise to an apparent constraint if the deformations were limited in extent. This model predicts that the
displacement between two points resulting from an elastic
deformation of the entire nucleus will be proportional to
the distance between the points. However, when the
average magnitude of the displacements 〈|d(t) – d(t + ∆t)|〉
was plotted against the distance d(t), for a fixed time interval ∆t = 24 seconds, no such correlation was seen (data not
shown). Hence, the observed motions are unlikely to
result from a simple elastic deformation.
Chromatin motion does not require active metabolism
What is the physical basis of chromatin motion? The
random walk motion could be due either to Brownian
motion, involving collisions with thermally excited solvent
particles, or else it could be driven by enzymes or motor
proteins. The answer is not obvious because, in addition
to the enzymes of DNA metabolism which can act as
force-producing motors [16], the nucleus contains a number of potential ATPases, such as the structural maintenance of chromosomes (SMC) family of proteins [17,18],
thought to produce conformational changes (and hence
motion) in chromatin. Conventional motor proteins, including myosin/actin-related proteins [19,20] have also been
identified in the nucleus. If interphase chromatin motion
is due to the action of such mechanoenzymes, active
metabolism would be required to support the movements.
To test a requirement for metabolic activity, we repeated
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Figure 3
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〈∆d2〉 against ∆t (Figure 2c). We expected that the
plasmid, being much smaller than a chromosome, should
have a much higher diffusion constant. Surprisingly, the
diffusion constant for the plasmid was 3× 10–12 cm2/second,
slightly less than that for a chromosome. Thus, contrary to
expectation, loci on shorter pieces of chromatin do not
necessarily diffuse faster than loci on longer ones. But
plasmid chromatin was found to be confined just like an
entire chromosome. If confinement of diffusion in fact
reflects tethering of discrete chromosome sites to an
immobile structure, then the diffusion constant would
depend not on the overall size of the chromosome but
only on the length of chromatin between successive
tethering points.
Current Biology
Confinement of diffusion is microtubule-dependent
Confinement of chromatin is dependent on microtubules. Open circles,
motion in cells treated with 15 µg/ml nocodazole in YPD medium.
Closed circles, untreated cells. Solid line, best-fit curve derived by
computer simulation using D = 5 × 10–12 cm2/sec, R = 0.3 µm for the
untreated cells. Broken line, best-fit curve using D = 3 × 10–12 cm2/sec,
R = 0.7 µm for the nocodazole data. In the presence of nocodazole, the
confinement radius shifts from 0.3 µm, corresponding to a volume of
0.11 µm3, to 0.7 µm, corresponding to a volume of 1.4 µm3, which
represents a 10-fold expansion of the confinement region.
the motion measurement following incubation in, and in
the continued presence of, 0.02% azide, which poisons
cellular metabolism by blocking the respiratory electron
transport chain. This concentration of azide is lethal and
immediately arrests cell division and mitotic chromosome
movements (data not shown) as well as other types of
intracellular motility in yeast [21]. As illustrated in Figure
2b, diffusion of chromatin is only slightly reduced in the
presence of this lethal dose of azide. Because chromatin
motion continues in the absence of active metabolism, it is
likely that it reflects true Brownian motion.
Constrained diffusion suggests that chromatin is tethered
to an immobile structure, but the identity of this structure
is unknown. To test whether microtubules play a role in
confining chromatin, we treated yeast cells with nocodazole. As seen in Figure 3, when microtubules were depolymerized with nocodazole, chromatin diffusion was
much less confined, and there was an expansion of the
confinement region. This surprising result suggests that
microtubules play a role in chromatin confinement, either
through a direct interaction between interphase chromatin
and intranuclear microtubules or more indirectly through
an interaction of nuclear structures with cytoplasmic
microtubules. Microtubules are not generally thought to
be present in interphase nuclei, although intranuclear
microtubules have been observed in interphase in some
fungi [23]. In either case, the fact that chromatin confinement can be removed or reduced by pharmacological
treatment verifies the existence of actual confinement by
demonstrating that the chromatin has the capacity for
unconfined motion.
Chromatin diffusion is independent of chromosome size
Drosophila chromatin also undergoes constrained
diffusion
Diffusional mobility generally depends on the size of the
diffusing object. If chromatin motion depends on chromosome size, large and small chromosomes or plasmids
would differ in their ability to move around in the
nucleus, and hence in their ability to participate in interactions like recombination that require motion. A dependence of chromosome mobility on size is very much to be
expected. The diffusion of tracer molecules in the cytoplasm depends strongly on the size of the molecules [22].
To determine how a chromosome’s size affects its diffusional mobility in the nucleus, we measured the motion
of a small circular centromere-containing plasmid. We
used a 15 kilobase (kb) plasmid containing a centromere
sequence (CEN); 10 kb of the plasmid was lac operator
repeats and thus most of the plasmid could be visualized.
Cells carrying two copies of the plasmid and thus showing
two distinct spots of fluorescence were used to compute
To ascertain the generality of the phenomenon of constrained diffusion of chromatin, we measured chromatin
motion in D. melanogaster by exploiting the specific localization pattern of topoisomerase II. In Drosophila, topoisomerase II accumulates primarily at one or two discrete foci
per nucleus [9]. To test whether these foci reflect sitespecific chromosome binding, immunofluorescence was
carried out in Drosophila embryos [24] using anti-topoisomerase II antibodies, following fluorescence in situ
hybridization (FISH) using DNA probes to heterochromatic satellite regions [25]. The topoisomerase II spot did
not coincide with the rDNA locus or the Responder of
segregation distorter (Rsp) heterochromatin block, but colocalized precisely with the 359 base pair (bp) repeat block
[26,27] on the X chromosome (Figure 4). The positions
and shapes of the FISH and immunofluorescence signals
exactly coincide, implying that topoisomerase II binding is
Research Paper Dynamics of nuclear architecture in vivo Marshall et al.
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Figure 4
Visualizing interphase chromatin motion in
Drosophila. Topoisomerase II binds at the
359 bp repeat region on the X chromosome in
Drosophila embryos. (a) Heterochromatin of
the X chromosome [27]. (b–e) Simultaneous
fluorescent in situ hybridization (FISH) and
immunofluorescence demonstrating
topoisomerase II accumulation at the 359 bp
repeat in anaphase. (b) Anti-topoisomerase II
immunofluorescence. (c) FISH using a probe
to the rDNA locus (d) FISH using probe to the
359 bp repeat. (e) overlay of (b), (c) and (d).
Clearly, the topoisomerase II signal completely
coincides with the 359 bp signal but not with
the neighboring rDNA. Bar = 2.0 µm. (f–h)
Topoisomerase II localization in interphase. (f)
anti-topoisomerase II immunofluorescence. (g)
FISH using a probe to the 359 bp repeat. (h)
Overlay showing complete coincidence of the
two signals. Bar = 2.0 µm. (i) Injection of
rhodamine-labeled topoisomerase II allows
visualization of the 359 bp repeat region in
vivo in three dimensions. Times corresponding
to each stereo pair are given in seconds.
Bar = 2.0 µm. Embryos imaged under these
conditions remain viable: after imaging,
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embryos were maintained in humidified
chambers until hatching. Embryos that were
imaged hatched with the same frequency as
embryos injected with buffer and not imaged.
During imaging, synchronized mitoses
co-extensive with the entire 359 bp repeat region. In
agreement with these findings, the most common topoisomerase II-specific drug-stimulated cleavage site in the
Drosophila genome is found in the 359 bp repeat sequence
[28]. Thus, topoisomerase II is one of a growing number of
proteins known to bind to specific heterochromatic
regions [29,30]. This localization provides a means of
tracking a specific chromosome region: by injecting fluorescently labeled topoisomerase II into living embryos [9]
the foci of topoisomerase II accumulation can be imaged,
revealing the motion of the underlying chromatin (Figure
4i). Embryos remained alive during imaging as judged by
the occurrence of normal synchronized nuclear divisions
and subsequent successful hatching.
To compensate for nuclear drift, we computed the distance r(t) from the topoisomerase II spot to the center of
the nucleus (Figure 5a). For a particle with diffusion constant D, a plot of 〈∆r2〉 against ∆t should be linear with
slope 2D. Just as in the case of two diffusing particles,
confinement will cause the plot to reach a plateau at large
time intervals. We plotted 〈∆r2〉 against ∆t for 27 nuclei
from six different Drosophila embryos (Figure 5b). The
data are best fit by simulations of a diffusing particle with
a diffusion constant D = 2.0 × 10–11 cm2/sec, a slightly larger
value than in yeast, and a confinement radius of 0.9 µm.
This confinement is interesting because the 359 bp repeat
is a scaffold-associated region (SAR) in Drosophila [28],
and may thus reflect the attachment of chromatin to an
internal nuclear skeleton [31].
occurred on schedule and no chromosome
segregation defects such as anaphase
bridges were observed.
Discussion
Comparison with other studies of chromatin motion
Previous studies of chromatin in living cells using timelapse microscopy have generally indicated that rotational
motion of the nucleus is the predominant type of chromatin motion [4,5]. Our study differs from these studies in
that we have deliberately chosen to use rotationally invariant measures (d and r), so that changes of position within
the nucleus, rather than overall nuclear rotation, can be
measured directly. Apart from nuclear rotation [4,5],
apparent Brownian motion of chromosomes within the
nucleus has not been reported previously. The small diffusion constants measured here, together with the finding
that chromatin diffusion is constrained, makes the diffusive motion unlikely to be noticed unless explicitly tested
for, using the type of analysis employed here.
A recent study has used FRAP to measure chromatin diffusion in cells in culture [2]. Nuclei labeled with an intercalating DNA stain were photobleached by a laser beam
focused to a spot of 0.8 µm diameter and, after bleaching,
the time-course of recovery of fluorescence was measured.
Because the recovery of fluorescence was incomplete, it
was concluded that chromatin was not mobile. Our
approach of directly tracking chromatin motion, with the
finding that chromatin undergoes confined diffusion,
allows us to suggest a different interpretation for the
FRAP data. Chromatin diffusion is confined to spatial
scales less than 0.3 µm (the size of the confinement
region), a conclusion also reached by FRAP. On smaller
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Figure 5
(a)
Comparison of chromatin diffusion with predictions from
theoretical polymer dynamics
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Chromatin diffusion in Drosophila. (a) plot of distance r from the center
of the nucleus to the topoisomerase II spot, over time, for a single
nucleus. (b) Mean-squared change in distance plotted against time
interval. Solid circles, data from living embryos. A total of 27 data
records, each containing an average of nine time points, were
combined in this plot. Solid line, the best-fit simulation result
corresponding to D = 2.0 × 10–11 cm2/sec and R = 0.9 µm. Open
circles, fixed embryos stained with anti-topoisomerase II antibodies and
imaged under identical conditions.
scales — inaccessible to FRAP because of the relatively
large size of the bleached spot but measurable by our
direct tracking approach — the chromatin is in fact fully
capable of diffusional motion, as required for the dynamic
functional behavior of chromatin.
Comparison of chromatin diffusion with the diffusion of
other biopolymers
Chromatin moves with a diffusion constant much lower
than that previously reported for biological macromolecules.
Proteins have diffusion constants around 10–6 cm2/second in
aqueous solution and 10–8 to 10–7 cm2/sec in cytoplasm
[32]. The slower diffusion of chromatin is not surprising
given the extremely large size of an interphase chromosome. Chromatin also diffuses more slowly than DNA in
dilute solution, which has a diffusion constant ranging
from 10–8 to 10–9 cm2/sec for DNA that is 4 to 300 kb in
length [33]. The high concentration of chromatin within
the nucleus would predict that chromatin in situ should
have more difficulty diffusing than does DNA in dilute
solution.
We next compare the diffusion constant of chromatin with
that expected for a large polymer in free solution [34] in
which Dfree = 0.2 kT/ηR where kT = 4 × 10–14 erg at room
temperature, η is viscosity, and R is average end-to-end
polymer length. For the CEN plasmid, an approximation
for R is the radius of the GFP signal, which is less than
0.5 µm: this upper limit on R provides a lower limit for
Dfree. Nucleoplasm viscosity is in the range 1.0–10.0 cP
[35,36]. A value of η = 5 cP gives a minimum D value
of 3 × 10–9 cm2/sec, which is three orders of magnitude
larger than the experimental value. This discrepancy is
difficult to reduce with reasonable changes in R or in η.
But chromatin is not in dilute solution. As with other
macromolecules [22], crowding and entanglement will
impede chromatin motion. We can estimate these effects
on the basis of the theory of reptation [37], assuming that
chromatin is a random polymer [38] entangled with itself
and with other chromatin polymers. The entanglements
delimit a tube within which the polymer diffuses with diffusion constant Dt. The n entanglement sites per chain
divide it into n subchains, each with average radius
Rsub = R/(n1/2), so each subchain has diffusion constant
Dfreen1/2. A string of n subchains thus diffuses through the
tube with diffusion constant Dt ~ (1/n)Dfreen1/2 = Dfree/n1/2.
The time τ* to diffuse out of the tube is τ* = L2/Dt where
the tube contour length is L = nRsub. Simultaneously, the
center of mass of the polymer diffuses a distance R.
Hence, Dentangled ~ R2/τ* = R2Dt/L2 = Dt/n (since L2 = nR2),
so the final diffusion constant Dentangled = Dfree/n3/2. A
modest number (n~20) of entanglements would reduce
the diffusion constant by two orders of magnitude. The
observed D value is thus consistent with Brownian motion
of an entangled polymer.
Diffusion-driven mechanisms for processes that require
chromosome motion
Many essential processes require interphase chromosomes
to move over significant distances within the nucleus.
Examples include meiotic homolog pairing, somatic
recombination and chromosome condensation. In imagining possible mechanisms for these processes, we consider
two general classes: diffusion-driven mechanisms and
mechanisms that rely on active motility. A well-known
example of the latter is mitosis, in which a microtubulebased motility system is used first to drive chromosomes
to the metaphase plate and then to segregate them to the
spindle poles. Other processes, such as homolog pairing or
recombination, which involve chromosome movements of
a comparable magnitude, may also depend on active
mechanisms.
The alternative to active motility is a diffusion-driven
mechanism that would require two chromatin sites to be
driven by thermal motion until they collide at random and
Research Paper Dynamics of nuclear architecture in vivo Marshall et al.
then interact. Most protein–protein or protein–DNA interactions are diffusion-driven but, as noted above, the diffusion constants for proteins, even in the crowded conditions
of living cytoplasm, are generally high enough for diffusion-driven mechanisms to be effective. We are thus left
with a straightforward quantitative question: is chromatin
diffusion sufficiently fast to be effective, or given the
small chromatin diffusion constant, is some other active
mechanism operating? A process such as recombination
might entail chromatin movements of several micrometers. Given a diffusion constant in the range 10–12 to
10–11 cm2/sec, it would take roughly one to ten minutes for
chromatin to diffuse 1 µm, which is sufficiently fast compared to the duration of interphase (greater than one
hour). We conclude that diffusion-driven mechanisms for
processes requiring chromatin motion are compatible with
the measured rate of chromatin diffusion.
Confinement of diffusion
Constrained diffusion has important implications for
nuclear processes involving motion. For two loci to interact, their confinement regions must overlap, or else the
interaction will be prevented because the loci will never
be sufficiently close. On the other hand, if the confinement regions of two loci do overlap, the frequency of collisions between the loci will actually be higher than if the
loci were unconfined, because they will be forced to
remain in the same general vicinity. Thus, as a result of
constrained diffusion, nuclear architecture, which fixes the
positions of loci in the nucleus, becomes a dominating
factor in determining whether a particular interaction can
or cannot occur. A picture thus emerges of interphase
chromatin being able to diffuse within the nucleus, but
only to a limited extent. This result is consistent with our
recent studies of nuclear positioning during interphase in
Drosophila, which indicated that, for 42 different loci
examined, each was consistently found in approximately
the same locus-specific position in all nuclei [39].
The alleviation of confinement by nocodazole suggests
that microtubules play some role in chromatin confinement. We note however that in yeast, the tagged site is
near a centromere, and if confinement reflects a direct
interaction of the centromere with interphase microtubules that are nucleated by the spindle pole body, this
could explain the effect of nocodazole treatment. Microtubule-dependent confinement could thus be a consequence of the closed mitosis of yeast, in which the spindle
pole body remains embedded in the nuclear envelope. It
is unclear whether this microtubule dependence will be a
general feature of chromatin motion in other cell types.
Although confinement may reflect physical interaction
with the nuclear envelope, spindle pole body or nuclear
matrix, it may simply reflect the limited interstitial space
between chromatin fibers. We can apply Ogston’s [40]
937
formula to determine the average void space in a solution
of random fibers, 〈R〉 = (4L)–1/2 where L is the average chain
density. Given a contour length of 75 µm if the 25
megabase diploid yeast genome is packed as a 30 nm fiber,
and given a nuclear radius 1.5 µm, we get L = 5 µm–2.
Thus, the average gap 〈R〉 between fibers is 0.2 µm and is
similar to the observed confinement radius. The exact
nature of the confinement is thus unclear and could reflect
either tethering to a structure or crowding by neighboring
chromatin chains. This question will be the subject of
future experiments.
Measurement of physical properties from motion in living
cells
Many processes in cell biology, such as chromosome segregation or intracellular transport of vesicles and
organelles, are essentially mechanical. In such cases, the
mechanical properties of the relevant cellular structures
are of fundamental importance. Direct measurement of
properties such as rigidity, viscosity or diffusional mobility
could, in principle, be made using isolated cellular components in vitro, but the cellular environment is likely to
strongly influence the physical behavior of such largescale structures. This is particularly true of chromatin, the
conformation of which is notoriously sensitive to the
buffer conditions used for isolation. Clearly, an ideal
approach would be to make mechanical measurements
inside the living cell using minimally invasive means.
Physical manipulation within living cells using microneedles [41] or laser tweezers [42] has proven an invaluable tool for understanding chromosome motion during
mitosis, but in situations in which the cellular structures
are too small, too delicate, too densely packed or otherwise inaccessible to micromanipulation procedures, an
approach based on pure observation is highly desirable. As
illustrated by the present study, three-dimensional timeresolved visualization of movements of cellular structures
in living cells, when coupled with quantitative motion
analysis, provides a powerful tool for measuring mechanical behavior while minimizing perturbation of the cell.
This approach of inferring mechanistic behavior from
analysis of motion, which has played an exceedingly
important role in physics and astronomy, should, with the
advent of routine three-dimensional microscopy and
quantitative motion analysis, be applicable to a broad
range of problems in cell biology.
Conclusions
Our primary conclusion is that interphase chromatin
undergoes constrained Brownian motion. A segment of
chromatin is confined within a small subregion of the
nucleus, representing roughly one percent of the nuclear
volume, and cannot move out of this region of confinement; but within this region, the chromatin segment
undergoes diffusive motion with a diffusion constant in
the range 10–12 to 10–11 cm2/sec. The simplest model is
938
Current Biology, Vol 7 No 12
that this confinement reflects the attachment of chromatin
to an immobile superstructure in the nucleus, which then
confines the segment of chromatin between successive
attachment points. A series of such attachment points distributed along a chromosome — for example, the set of
nuclear envelope association sites present in Drosophila
[39] — would thus partition the chromosome into a set of
domains [43,44], each reflecting a confinement region.
This model has important implications for our understanding of processes involving chromatin motion, such as
recombination or homology searching. As long as the confinement regions for two chromosome segments are overlapping, Brownian motion of the chromatin within those
regions will be fast enough to allow a diffusion-driven
interaction between them to take place on a reasonable
time scale. If the two confinement regions do not overlap,
however, then an interaction between the two chromosome segments will be effectively prevented. Constrained
diffusion therefore provides a mechanism by which
nuclear architecture exerts a kinetic control over chromosome interactions.
Materials and methods
In vivo imaging of chromatin motion in S. cerevisiae
Cells were grown and mounted as described [7]; such cells grow and
divide normally. Time-lapse three-dimensional images were collected at
rates of one three-dimensional data set every 12 sec, 24 sec or 96 sec,
by wide-field deconvolution three-dimensional microscopy [45] using a
60 × N.A. 1.4 objective and 1.5180 oil. At each time point, fourteen 256 × 256 pixel images were collected at focal plane increments
of 0.25 µm per plane.
Simulation of constrained random walk motion
Random walks were simulated on a cubic lattice [46] for two particles.
Every time step (τ = 50 msec), x, y and z coordinates of the particle
were independently increased or decreased (with equal probability) by
δ = 2Dτ. To represent confinement, steps causing a particle to exceed
a confinement distance of R from its initial position were rejected, and a
new step chosen. The distance d(t) between the two particles was
stored every 5 sec of simulation, with 1800 steps stored per run. Finally,
200 runs were averaged to compute a plot of 〈∆d2〉 against ∆t. Simulations were run for different values of D and R, changing D in increments
of 0.5 × 10–12 cm2/sec and R in 0.025 µm increments. For each set of
values, observed data and the simulation were compared, and the D
and R values resulting in the least squared error were chosen. For
Drosophila data, simulations were carried out using only a single diffusing particle and taking distance from a fixed reference point.
Estimation of distance measurement error
We approximate the observed distance d(t) as the actual distance d′(t)
plus a zero-mean random offset δ, and define root mean square (r.m.s.)
error in distance measurement to be √〈∆d2〉. Clearly 〈∆d(∆t)2〉
approaches 2〈δ2〉 when ∆t (and hence ∆d′) becomes small. To find an
upper limit on δ, we note that 2〈δ2〉 ≤ 〈∆d(∆tmin)2〉 where ∆tmin is the
smallest measured time interval. For the fixed cell data of Figure 2b,
∆tmin = 12 sec, and the corresponding 〈∆d(∆tmin)2〉 is approximately
0.004 µm2. We conclude that the r.m.s. distance measurement
precision √〈∆d2〉 ≤ 0.04 µm.
Azide treatment of S. cerevisiae cells
Following induction of GFP–LacI, sodium azide was added from a
10% stock solution to give a final concentration of 0.02%. Cells were
then incubated in azide for 20 min, then mounted and observed in the
continuous presence of azide. Data from 30 cells with an average of 31
time points per data record were combined and plotted in Figure 2b.
Growth curves were carried out in the presence and absence of azide
and indicated a complete arrest of cell division in the azide-treated
cells. The effect of azide on metabolism and active motility is very rapid:
addition of 0.02% azide to cells undergoing mitotic division results in
an immediate arrest of mitotic chromosome movement; azide addition
similarly results in immediate arrest of movements of cortical actin
patches in yeast [21].
In vivo imaging of chromatin motion in Drosophila
Topoisomerase II injection and imaging were previously described [9].
Three-dimensional images were collected from cycle 12 or 13
embryos, by wide-field deconvolution microscopy [45], using a 60 ×
N.A. 1.4 objective lens and 1.5180 oil. At each time point, a set of 16
256 × 256 pixel images were collected at focal plane increments of
0.5 µm. One three-dimensional dataset was collected every 20 sec.
The nuclear center was defined as the centroid of the nuclear boundary
traced from the outline of the nuclear image. The topoisomerase II
focus position was defined by interactively picking the spot and taking
an intensity-weighted center of mass around the chosen point.
Acknowledgements
The authors thank J. Kilmartin, J. Haber, B. Scalettar, C. Coppin, M. Gustafsson and M. Lowenstein for valuable discussions. We also thank J. Haber,
Z. Kam, H. Bass, A. Franklin and members of the Sedat Lab for critical
reading of the manuscript. Anti-topoisomerase II antibodies were the kind
gift of Neil Osheroff, Vanderbilt University. This work was supported by NIH
grants GM-43987 and GM-225101-16 to A.W.M. and J.W.S. respectively.
D.A.A. is an investigator of the Howard Hughes Medical Institute. A.W.M. is
a David and Lucille Packard Fellow. W.F.M. was supported by a Howard
Hughes Medical Institute Predoctoral Fellowship.
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